Analysis of Wavelet Denoising with Different Types of Noises

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1 International Journal of Current Engineering and Technology E-ISSN , P-ISSN INPRESSCO, All Rights Reserved Available at Research Article Kishan Shivhare * and Gaurav Bhardwaj ECE Department, RJIT BSF Academy, Tekanpur, Gwalior, M.P., India Accepted 20 Dec 2016, Available online 21 Dec 2016, Vol.6, No.6 (Dec 2016) Abstract There are several types of noises those affect quality of an image such as Salt & pepper noise, Poisson noise, Gaussian noise, Speckle noise etc. Wavelet is a powerful tool for denoising a variety of signals. Here an image of a college building has been taken for denoising purpose with the help of HAAR Transform. The noisy image is first decomposed into five levels to obtain different frequency bands. Then first soft and hard methods are saperately used to remove the noisy coefficients by fixing the optimum value at 0.15 and then both of s are used in hybrid manner. In this paper, analysis of a colored image is carried out with four different noises at zero mean and at 0.02 variance that are applied on the image to produce noisy images. In order to enhance the quality of the noisy images, performance parameters of denoised images must be estimated. The comparison between different denoised image is taken in terms of MSE (mean square error), PSNR (peak signal to noise ratio), RMSE (root mean square error), SNR (signal to noise ratio) and SSIM (structural similarity index). Keywords: Salt & noise, Speckle noise, Gaussian noise, Poisson noise, Discrete Wavelet Transform, Soft,, SNR, PSNR, SSIM, MSE, RMSE. 1. Introduction 1 An image is mostly affected by noise produced by the sensor and circuitry of a scanner or digital camera. The denoising process is to remove the noise with retaining and not distorting the quality of processed image. Denoising analysis of the images is done by using Discrete Wavelet Transform (DWT). The experiments are conducted on a building image (.jpg format). Simple denoising algorithms which use DWT consist of three steps: 1) Discrete wavelet transform is adopted to decompose the noisy image and get the wavelet coefficients. 2) These wavelet coefficients are denoised with wavelet threshold. 3) Inverse transform is applied to the modified coefficients and get denoised image. The wavelet transform is better than Fourier transform because it gives frequency representation of the signal at any given interval of time, but Fourier transform gives only the frequency- amplitude representation of the signal but the time information is lost. Original Image Noise Noisy Image Discrete Wavelet Transform Thresholding / Shrinkage Inverse Wavelet Transform Thresholding is a simple non-linear technique which operates on one wavelet coefficients at a time. Each coefficient is thresholded by comparing threshold level. When a coefficient is smaller than threshold level then it is set to zero otherwise it is kept as it is or it is modified. *Corresponding author Kishan Shivhare is a M.Tech Student; Gaurav Bhardwaj is working as Assistant Professor De-noised Image Fig.1 Image denoising based on Wavelet Transform So we use Wavelet transform instead of the Fourier transform where we need time as well as frequency information at particular time. The fundamental idea behind wavelet coefficients is to analyze the signal at 2212 International Journal of Current Engineering and Technology, Vol.6, No.6 (Dec 2016)

2 different scales or resolutions, which is called multiresolution. The most important feature of wavelet transform is that it allows multiresolution decomposition. The wavelet transform is good at energy compaction. The small coefficients are more likely due to noise and large coefficients are more likely due to important signal features. These small coefficients can be thresholdeded without affecting the significant features of the image. Noise is a random variation of image Intensity and visible as small particles in the image. It may arise in the image as effects of basic physics-like photon nature of light or thermal energy of heat inside the image sensors. Here we are discussing about four types of noise and their effect on the image signal. 1) Gaussian noise 2) Speckle noise 3) Salt-and-pepper noise 4) Poisson noise Gaussian noise is a statistical noise having a probability density function (pdf) equal to the pdf of the normal distribution, which is also known as the Gaussian distribution. This is an additive noise model in nature. Additive white Gaussian noise (AWGN) can be produced by poor quality image acquisition, noisy environment or internal noise in communication channels. Speckle-noise is a granular noise in nature. It degrades the quality of the active radar, synthetic aperture radar (SAR), and medical ultrasound images. Speckle noise occurs due to random fluctuations in the return signal from an object in a RADAR system. Salt-and-pepper noise is also called impulsive noise or spike noise. Any image which has been affected by salt and pepper noise shows dark pixels in bright area and bright pixels in dark area of the image. It has only two possible values, a high value and a low value. This noise occurs during analog-to-digital converter errors, bit errors in transmission. Poisson noise or Shot noise is an electronic noise which is generated by a Poisson process. Shot noise follows the particle nature of light. Poisson or shot photon noise is the noise that occurs when the number of photons sensed by a sensor is not sufficient to provide detectable statistical information. and vertical filters. The coefficients which are represented as sub bands LH1, HL1, and HH1 are detail images while coefficients which are represented as sub band LL1 is approximation image. To obtain the next level of the wavelet coefficients the LL1 sub band is further decomposed as shown in Figure 2(b). (a) One level (b) Two level Fig.2 Image Decomposition by using DWT As LL1 sub band provides the most like original picture that is why it is called the approximation sub band. It is obtained from low pass filtering in both directions. The other bands are called detail sub bands. The L and H filters as shown in Figure 3 are one dimensional low pass filter (LPF) and high pass filter (HPF) used for image decomposition. HL1 is called horizontal fluctuation as it comes from low pass filtering in vertical direction and high pass filtering in horizontal direction. LH1 is called vertical fluctuation as it comes from opposite to HL1. HH1 comes from high pass filtering in both the directions so it is called diagonal fluctuation. LL1 is further decomposed into 4 sub bands LL2, LH2, HL2 and HH2. The process is carried out until the fifth decomposition is reached. After L number of decompositions a total number of D(L) =3*L+1 sub bands are obtained. Therefore after 5 decompositions D(5) = 3*5+1 = 16 sub bands are obtained. Fig.3 Wavelet Filter Bank Decomposition (One level) 2. Discrete Wavelet Transform (DWT) In Discrete Wavelet Transform signal energy is in the form of a small number of coefficients. DWT of noisy image if consist of small number of coefficients then would have high value of SNR and vice versa. Using inverse DWT, image is reconstructed by removing the coefficients with low SNR. Time and frequency components are simultaneously provided by Wavelet transform. When DWT is applied to noisy image, it is spreaded into four sub bands as shown in Figure 2(a). These sub bands are formed by separable horizontal Fig.4 Wavelet Filter Bank Reconstruction (One level) 2213 International Journal of Current Engineering and Technology, Vol.6, No.6 (Dec 2016)

3 A reverse process is shown in figure 4 which is used to reconstruct the decomposed image. Here, the L and H filters represent low pass reconstruction and high pass reconstruction filters respectively. 3. Wavelet Thresholding Thresholding technique operates on wavelet coefficients. It uses one of the wavelet coefficients at a time. In this process the coefficient which is smaller than the threshold value is set to zero otherwise the coefficient is kept or may be modified. If the coefficient has small value then it carries more noise than a large valued coefficient. While if it has large value then coefficient carries more signal information than small valued coefficients. Therefore noise coefficients or small valued coefficients below a certain threshold value are replaced by zero and an inverse wavelet transform may lead to a reconstruction that has lesser noise. Firstly wavelet analysis of a noisy image up to level N is done with of the each detail coefficients from level 1 to N and then signal is synthesized by using the altered detail coefficients from level 1 to N and approximation coefficients of level N. There are two types of ; 1) technique 2) Soft technique 3.1 technique shrinks the coefficients which have magnitudes below the threshold level, and leaves the rest of the coefficients unchanged. To suppress the noise we apply hard on each wavelet coefficients: F(X) = X I( X > t) Here t is a certain threshold and x is the coefficient. 3.2 Soft technique Soft technique extends hard technique by shrinking the magnitude of the remaining coefficients by t factor and producing a smooth rather than abrupt transition to zero. S(x) = sign(x)( x t) I( x > t) 4. Performance Parameters For comparing original building image with different denoised images, we calculate following parameters: 1) Mean Square Error (MSE): The MSE is the cumulative square error between the synthesized image and the original image defined by: ( ) ( ) 2 Where f is the original image and g is the synthesized image. MSE should be as low as possible. 2) Peak signal to noise ratio (PSNR): PSNR is the ratio between maximum possible power of a signal and the power of distorting noise which affects the quality of the original signal. It is defined by: ( ) Where MAX F is the maximum signal value that exists in our original image. PSNR should be as high as possible. 3) Root mean square error (RMSE): It measures of the differences between value predicted by a model or an estimator and the values actually observed. It is the square root of mean square error. RMSE should be as low as possible. 4) Structural Similarity Index (SSIM): It is a method for measuring the similarity between two images. The SSIM measure the image quality based on an initial distortion-free image as reference. ( ( ) ) ( )( ) ( )( ) Where n is the length of the input vector and σ 2 is the variance of the noise. Where: μ x is average of x; μ y is average of y; is variance of x; is variance of y; is covariance of x and y; Fig.5 and Soft Thresholding C 1 = (k 1L) 2 and C 2 = (k 2L) 2 are two variables to stabilize the division with weak denominator. L is the dynamic range of the pixel-values k 1 = 0.01 and k 2 = 0.03 by default. 5) Signal to noise ratio (SNR): Signal-to-noise ratio is defined as the power ratio between a signal (meaningful information) and the noise (unwanted signal). It should be as high as possible International Journal of Current Engineering and Technology, Vol.6, No.6 (Dec 2016)

4 5. Methodology 1) A building image has been taken for denoising purpose in Wavelet Toolbox in MATLAB. Four different noises (Salt and pepper, Speckle, Gaussian and Poisson) are added one by one in the original image of dimensions 512x512 in.jpg format at zero mean and 0.02 variance. For denoising HAAR wavelet transform is applied on the noisy images of all the four different noises up to five levels. A constant threshold value is taken at these levels. Each coefficient of vertical, horizontal and diagonal details is thresholded using soft, hard and hybrid threshold by combining both hard and soft. As a result of inverse wavelet transform, we get these noise free images within vertical, horizontal and diagonal details. 2) Calculation of the performance parameters for analyse denoised images is performed in the terms as SNR, PSNR, SSIM, MSE and RMSE. (g) (i) (h) (j) 6. Result (k) (l) (a) (b) (c) (d) (m) (n) (e) (f) (o) (p) 2215 International Journal of Current Engineering and Technology, Vol.6, No.6 (Dec 2016)

5 (q) (r) Table 4 at zero mean and 0.02 variance and MSE MSE Salt & Speckle Gaussian Poisson Fig.6 (a) Color Image, (b) Gray Image, (c) Image after adding Salt & noise, (d) Image after denoised by Soft threshold, (e) Image after denoised by threshold, (f) Image after denoised by threshold, (g) Image after adding Speckle noise, (h) Image after denoised by Soft threshold, (i) Image after denoised by threshold, (j) Image after denoised by threshold, (k) Image after adding Gaussian noise, (l) Image after denoised by Soft threshold, (m) Image after denoised by threshold, (n) Image after denoised by threshold, (o) Image after adding Poisson noise, (p) Image after denoised by Soft threshold, (q) Image after denoised by threshold, (r) Image after denoised by threshold Table 1 at zero mean and 0.02 variance and SNR SNR Salt & Speckle Gaussian Poisson Table 2 at zero mean and 0.02 variance and PSNR PSNR Salt & Speckle Gaussian Poisson Table 3 at zero mean and 0.02 variance and SSIM SSIM Salt & Speckle Gaussian Poisson Table 5 at zero mean and 0.02 variance and RMSE RMSE Salt & Speckle Gaussian Poisson Conclusions According to results generated in this paper, the has good results in SNR and PSNR but has less error results. Therefore Thresholding can be used to get the more accurate results. Inspite of these the threshold value and the level of decomposition and reconstruction also play an important role in Wavelet denoising. References Prateek Kumar and Sandeep Agarwal, (2015), Analysis of Wavelet Denoising of a Colour Image With Different Types of, Int. Journal of Signal Processing, Image Processing and Pattern Recognition, Vol. 8 No. 6, pp V. Mahesh, M. Someswara Rao, Ch. Sravani, P. Durgarao and S. Venkatesh,(2014), An Effective Image Denoising Using Adaptive Thresholding In Wavelet Domain, Int. Journal of Engineering Research and Applications ISSN : , vol. 4, no. 4 (Version 1), pp A. K. Das,(2014), Review on Image Denoising Techniques, International Journal of Emerging Technology and Advanced Engineering Website: (ISSN , ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014) , vol. 4, no. 4 (Version 1), pp V. Sharan, N. Keshari and T. Mondal,(2014), Biomedical Image Denoising and Compression in Wavelet using MATLAB, International Journal of Innovative Science and Modern Engineering (IJISME) ISSN: , vol. 2, no. 6. A. Vishwa and V. Goyal,(2013) An Improved Threshold Estimation Technique for Ultrasound Image Denoising, International Journal of Advanced Research in Computer Science and Software Engineering Research Paper, vol. 3, ISSN: X Available online at: International Journal of Current Engineering and Technology, Vol.6, No.6 (Dec 2016)

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